A Steiner triple system is a set of triples (subsets of
${1,2,dots,n}$) such that every pair is in exactly one triple. A partial parallel class in a Steiner triple system is a subset
of its triples that are pairwise disjoint. The chromatic index
of a Steiner triple system is the smallest number of partial parallel
classes into which its blocks can be partitioned.
It has been conjectured that every Steiner triple system of order
$v
eq 7$ has chromatic index at most $({v+3})/{2}$ when
$v equiv3 mod{6}$ and at most $({v+5})/{2}$ when $v equiv 1 mod{6}$.
We construct a Steiner triple system of order $v$ with chromatic index
at least ...